Why is my brakes making this loud squealing sound

Brake noise is the result of minute vibrations occurring at the brake pads where they contact the brake rotors and how they sit inside the brake calipers. Any unwanted movement at all can and often will create resonating noise. That said, if the brakes have been inspected, they are "safe" per the dealership technician. You could certainly resurface brake rotors and replace brake pads -- if that's all it requires -- and the noise will likely dissipate. However, even that may be temporary due to the condition of all components. Some noise can be considered "normal" - so be aware of that.